Find the loop invariant of the code where n 1). Algorithm 1 sum (int n) p=0 i=0 while in do p=p+2*i i++ end while return p (a) (4 points) What does the loop do? Write down a formula with the variable n. Prove the correctness of the loop invariant. (b) (4 points) Basis step (when n = 1): (c) Inductive step: i. (3 points) What is your inductive hypothesis? ii. (3 points) What are you trying to prove? 4 iii. (6 points) Complete the proof: